LSP is the first knowledge distillation module specifically designed for GNNs, which forces the local structure of the graph data learned by the student model to be similar to that of the teacher model [1]}.
The similarity \(L_{i,j}\)  between each node \(i\)  and its neighbor nodes \(j|\left(i,j\right)\in \varepsilon \)  in the feature space is calculated with one of the following kernel functions and then normalized with a softmax function
\(D\left(z_{i},z_{j}\right) ={\left\lbrace \begin{array}{ll}\left\Vert z_{i}-z_{j} \right\Vert _{2}^{2} & Euclidean \\z_{i}\cdot z_{j} & Linear \\\left(z_{i}\cdot z_{j}+c \right)^{d} & Poly\\e^{-\frac{1}{2\sigma }\left\Vert z_{i}-z_{j} \right\Vert ^{2}} & RBF\end{array}\right.}\) 
\(L_{i,j} = \frac{e^{D\left(z_{i},z_{j}\right)}}{\sum _{j|\left(i,j\right)\in \varepsilon \, \left(e^{D\left(z_{i},z_{j}\right)}\right)}}\,,\) 
